{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using ReinforcementLearningAnIntroduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the `MountainCar` in the `RLIntro` is a slightly different different from the one in `ReinforcementLearningEnvironments`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Plots\n",
    "\n",
    "using StatsBase\n",
    "\n",
    "using SparseArrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MountainCarEnv(-0.45872013821353175, 0.0)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "env = MountainCar.MountainCarEnv()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MultiContinuousSpace{Array{Float64,1}}([-1.2, -0.07], [0.5, 0.07])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "obs_space = get_observation_space(env)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "na = length(get_action_space(env))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8-element Array{Tiling{2,StepRangeLen{Float64,Base.TwicePrecision{Float64},Base.TwicePrecision{Float64}}},1}:\n",
       " Tiling{2,StepRangeLen{Float64,Base.TwicePrecision{Float64},Base.TwicePrecision{Float64}}}((-1.2:0.2125:0.7125, -0.07:0.0175:0.0875), [1 10 … 64 73; 2 11 … 65 74; … ; 8 17 … 71 80; 9 18 … 72 81])                 \n",
       " Tiling{2,StepRangeLen{Float64,Base.TwicePrecision{Float64},Base.TwicePrecision{Float64}}}((-1.2265625:0.2125:0.6859375, -0.0721875:0.0175:0.0853125), [1 10 … 64 73; 2 11 … 65 74; … ; 8 17 … 71 80; 9 18 … 72 81])\n",
       " Tiling{2,StepRangeLen{Float64,Base.TwicePrecision{Float64},Base.TwicePrecision{Float64}}}((-1.253125:0.2125:0.659375, -0.074375:0.0175:0.083125), [1 10 … 64 73; 2 11 … 65 74; … ; 8 17 … 71 80; 9 18 … 72 81])    \n",
       " Tiling{2,StepRangeLen{Float64,Base.TwicePrecision{Float64},Base.TwicePrecision{Float64}}}((-1.2796875:0.2125:0.6328125, -0.0765625:0.0175:0.0809375), [1 10 … 64 73; 2 11 … 65 74; … ; 8 17 … 71 80; 9 18 … 72 81])\n",
       " Tiling{2,StepRangeLen{Float64,Base.TwicePrecision{Float64},Base.TwicePrecision{Float64}}}((-1.30625:0.2125:0.60625, -0.07875:0.0175:0.07875), [1 10 … 64 73; 2 11 … 65 74; … ; 8 17 … 71 80; 9 18 … 72 81])        \n",
       " Tiling{2,StepRangeLen{Float64,Base.TwicePrecision{Float64},Base.TwicePrecision{Float64}}}((-1.3328125:0.2125:0.5796875, -0.0809375:0.0175:0.0765625), [1 10 … 64 73; 2 11 … 65 74; … ; 8 17 … 71 80; 9 18 … 72 81])\n",
       " Tiling{2,StepRangeLen{Float64,Base.TwicePrecision{Float64},Base.TwicePrecision{Float64}}}((-1.359375:0.2125:0.553125, -0.083125:0.0175:0.074375), [1 10 … 64 73; 2 11 … 65 74; … ; 8 17 … 71 80; 9 18 … 72 81])    \n",
       " Tiling{2,StepRangeLen{Float64,Base.TwicePrecision{Float64},Base.TwicePrecision{Float64}}}((-1.3859375:0.2125:0.5265625, -0.0853125:0.0175:0.0721875), [1 10 … 64 73; 2 11 … 65 74; … ; 8 17 … 71 80; 9 18 … 72 81])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ntilings = 8\n",
    "ntiles = 8\n",
    "tiling = Tiling(Tuple(range(l, step=(h-l)/ntiles, length=ntiles+2) for (l, h) in zip(obs_space.low, obs_space.high)))\n",
    "offset = (obs_space.high .- obs_space.low) ./ (ntiles * ntilings)\n",
    "tilings = [tiling - offset .* (i-1) for i in 1:ntilings]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([1, 1, 1, 1, 1, 1, 1, 1], [81, 81, 81, 81, 81, 81, 81, 81])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "TilingPreprocessor(tilings)(obs_space.low), TilingPreprocessor(tilings)(obs_space.high)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([-1.2, -0.07], [0.5, 0.07])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(POSITION_MIN, VELOCITY_MIN), (POSITION_MAX, VELOCITY_MAX) = obs_space.low, obs_space.high"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By using `TilingPreprocessor`, we transform a state of two scalars (like `[-0.55, 0.0]`) to a vector of Int (like `[39, 40, 40, 40, 40, 40, 40, 40]`). To use the `LinearQApproximator`, we need to encdoe this new state together with an action into a feature vector:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8×81×3 LinearIndices{3,Tuple{Base.OneTo{Int64},Base.OneTo{Int64},Base.OneTo{Int64}}}:\n",
       "[:, :, 1] =\n",
       " 1   9  17  25  33  41  49  57  65  73  …  593  601  609  617  625  633  641\n",
       " 2  10  18  26  34  42  50  58  66  74     594  602  610  618  626  634  642\n",
       " 3  11  19  27  35  43  51  59  67  75     595  603  611  619  627  635  643\n",
       " 4  12  20  28  36  44  52  60  68  76     596  604  612  620  628  636  644\n",
       " 5  13  21  29  37  45  53  61  69  77     597  605  613  621  629  637  645\n",
       " 6  14  22  30  38  46  54  62  70  78  …  598  606  614  622  630  638  646\n",
       " 7  15  23  31  39  47  55  63  71  79     599  607  615  623  631  639  647\n",
       " 8  16  24  32  40  48  56  64  72  80     600  608  616  624  632  640  648\n",
       "\n",
       "[:, :, 2] =\n",
       " 649  657  665  673  681  689  697  …  1249  1257  1265  1273  1281  1289\n",
       " 650  658  666  674  682  690  698     1250  1258  1266  1274  1282  1290\n",
       " 651  659  667  675  683  691  699     1251  1259  1267  1275  1283  1291\n",
       " 652  660  668  676  684  692  700     1252  1260  1268  1276  1284  1292\n",
       " 653  661  669  677  685  693  701     1253  1261  1269  1277  1285  1293\n",
       " 654  662  670  678  686  694  702  …  1254  1262  1270  1278  1286  1294\n",
       " 655  663  671  679  687  695  703     1255  1263  1271  1279  1287  1295\n",
       " 656  664  672  680  688  696  704     1256  1264  1272  1280  1288  1296\n",
       "\n",
       "[:, :, 3] =\n",
       " 1297  1305  1313  1321  1329  1337  …  1897  1905  1913  1921  1929  1937\n",
       " 1298  1306  1314  1322  1330  1338     1898  1906  1914  1922  1930  1938\n",
       " 1299  1307  1315  1323  1331  1339     1899  1907  1915  1923  1931  1939\n",
       " 1300  1308  1316  1324  1332  1340     1900  1908  1916  1924  1932  1940\n",
       " 1301  1309  1317  1325  1333  1341     1901  1909  1917  1925  1933  1941\n",
       " 1302  1310  1318  1326  1334  1342  …  1902  1910  1918  1926  1934  1942\n",
       " 1303  1311  1319  1327  1335  1343     1903  1911  1919  1927  1935  1943\n",
       " 1304  1312  1320  1328  1336  1344     1904  1912  1920  1928  1936  1944"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "const STATE_INDICES = LinearIndices(\n",
    "    (\n",
    "        ntilings,\n",
    "        (ntiles+1)^2, # the maximum index among the elements of the preprocessed state\n",
    "        na,\n",
    "    )\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "encode_state_action (generic function with 2 methods)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "encode_state_action(state::Vector{Int}, action) = sparsevec([STATE_INDICES[i, s, action] for (i, s) in enumerate(state)], ones(length(state)), length(STATE_INDICES))\n",
    "encode_state_action(obs, action) = encode_state_action(get_state(obs), action)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "create_env_agent (generic function with 3 methods)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function create_env_agent(α=2e-4, n=0)\n",
    "    env = WrappedEnv(\n",
    "        env=MountainCar.MountainCarEnv(),\n",
    "        preprocessor=TilingPreprocessor(tilings) \n",
    "    )\n",
    "\n",
    "    agent = Agent(\n",
    "        policy=QBasedPolicy(\n",
    "            learner=TDLearner(\n",
    "                approximator=LinearQApproximator(\n",
    "                    weights=zeros(length(STATE_INDICES)),\n",
    "                    feature_func=encode_state_action,\n",
    "                    actions=collect(1:na)\n",
    "                    ),\n",
    "                optimizer=Descent(α),\n",
    "                n=n\n",
    "                ),\n",
    "            explorer=GreedyExplorer()\n",
    "            ),\n",
    "        trajectory=EpisodicCompactSARTSATrajectory(;state_type=Vector{Int})\n",
    "    )\n",
    "\n",
    "    env, agent\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "show_approximation (generic function with 1 method)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function show_approximation(n)\n",
    "    env, agent = create_env_agent()\n",
    "    run(agent, env, StopAfterEpisode(n))\n",
    "    [agent.policy.learner.approximator(env.preprocessor([p, v])) |> maximum\n",
    "        for p in range(POSITION_MIN, stop=POSITION_MAX, length=40),\n",
    "            v in range(VELOCITY_MIN, stop=VELOCITY_MAX, length=40)]\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
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     "execution_count": 13,
     "metadata": {},
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    }
   ],
   "source": [
    "heatmap(show_approximation(1))"
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  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": false
   },
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     "execution_count": 15,
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   ],
   "source": [
    "heatmap(show_approximation(104))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
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     "execution_count": 16,
     "metadata": {},
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    "heatmap(show_approximation(1000))"
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  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": false
   },
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      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = plot(legend=:topright)\n",
    "n_runs = 10  # about 2 seconds per run, quite slow here, need revisit\n",
    "for α in [0.1/8, 0.2/8, 0.5/8]\n",
    "    avg_steps_per_episode = zeros(500)\n",
    "    for _ in 1:n_runs\n",
    "        env, agent = create_env_agent(α)\n",
    "        hook = StepsPerEpisode()\n",
    "        run(agent, env, StopAfterEpisode(500; is_show_progress=false),hook)\n",
    "        avg_steps_per_episode .+= hook.steps\n",
    "    end\n",
    "    plot!(p, avg_steps_per_episode ./ n_runs)\n",
    "end\n",
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "run_once (generic function with 1 method)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function run_once(α, n)\n",
    "    env, agent = create_env_agent(α, n)\n",
    "    hook = StepsPerEpisode()\n",
    "    run(agent, env, StopAfterEpisode(50),hook)\n",
    "    mean(hook.steps)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
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       "<polyline clip-path=\"url(#clip4402)\" style=\"stroke:#ac8d18; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
       "  229.132,929.708 366.584,1143.08 504.035,1005.62 641.486,1203.12 778.938,1080.24 916.389,250.324 \n",
       "  \"/>\n",
       "<path clip-path=\"url(#clip4400)\" d=\"\n",
       "M1905.6 493.644 L2280.76 493.644 L2280.76 130.764 L1905.6 130.764  Z\n",
       "  \" fill=\"#ffffff\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
       "<polyline clip-path=\"url(#clip4400)\" style=\"stroke:#000000; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
       "  1905.6,493.644 2280.76,493.644 2280.76,130.764 1905.6,130.764 1905.6,493.644 \n",
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       "<polyline clip-path=\"url(#clip4400)\" style=\"stroke:#009af9; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
       "  1929.6,191.244 2073.6,191.244 \n",
       "  \"/>\n",
       "<g clip-path=\"url(#clip4400)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 2097.6, 208.744)\" x=\"2097.6\" y=\"208.744\">n = 1</text>\n",
       "</g>\n",
       "<polyline clip-path=\"url(#clip4400)\" style=\"stroke:#e26f46; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
       "  1929.6,251.724 2073.6,251.724 \n",
       "  \"/>\n",
       "<g clip-path=\"url(#clip4400)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 2097.6, 269.224)\" x=\"2097.6\" y=\"269.224\">n = 2</text>\n",
       "</g>\n",
       "<polyline clip-path=\"url(#clip4400)\" style=\"stroke:#3da44d; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
       "  1929.6,312.204 2073.6,312.204 \n",
       "  \"/>\n",
       "<g clip-path=\"url(#clip4400)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 2097.6, 329.704)\" x=\"2097.6\" y=\"329.704\">n = 4</text>\n",
       "</g>\n",
       "<polyline clip-path=\"url(#clip4400)\" style=\"stroke:#c271d2; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
       "  1929.6,372.684 2073.6,372.684 \n",
       "  \"/>\n",
       "<g clip-path=\"url(#clip4400)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 2097.6, 390.184)\" x=\"2097.6\" y=\"390.184\">n = 8</text>\n",
       "</g>\n",
       "<polyline clip-path=\"url(#clip4400)\" style=\"stroke:#ac8d18; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
       "  1929.6,433.164 2073.6,433.164 \n",
       "  \"/>\n",
       "<g clip-path=\"url(#clip4400)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 2097.6, 450.664)\" x=\"2097.6\" y=\"450.664\">n = 16</text>\n",
       "</g>\n",
       "</svg>\n"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = plot(legend=:topright)\n",
    "for (A, n) in [(0.4:0.1:1.7, 1), (0.3:0.1:1.6, 2), (0.2:0.1:1.4, 4), (0.2:0.1:0.9, 8), (0.2:0.1:0.7, 16)]\n",
    "    plot!(p, A, [mean(run_once(α/8, n) for _ in 1:5) for α in A], label=\"n = $n\")\n",
    "end\n",
    "p"
   ]
  }
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